Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Methodology for building a functionally stable intelligent information system of a manufacturing enterprise
Get PDFThe article analyzes the concept of process management in an industrial enterprise, which provides functional stability of technological processes using information systems of various types and allows to increase productivity of all production centers while reducing the number of people employed in production and the impact of various destabilizing factors. The research of existing mathematical models of functionally stable complex technical systems and formalization of the main types of procedures of the process of functioning of the intellectual information system of the enterprise is carried out. The method of ensuring the properties of functional stability of the intelligent information system of the enterprise is improved by presenting the functioning of the system in the form of a formalized process, in which the main types of procedures are accumulation of tests, analysis of test links, diagnosing a failed module and restoring the system. This technique allows to ensure the property of functional stability of the information system of the enterprise.
Pages of the article in the issue: 116 - 127
Language of the article: Ukrainia
Radiation of a flat piston in a wedge-shaped waveguide
Get PDFIn the work the task of radiation of a at piston in a wedge-shaped waveguide is considered. The peculiarities of the radiation of a at piston into a wedge-shaped waveguide depending on the parametersof the task, namely, the angle of inclination of the wedge and the wave size of the piston, that is theratio of the piston length to the wavelength it emits, are investigated. The directional charts of a atpiston in a wedge-shaped waveguide at dierent angles of the wedge are calculated. It is shown that at acertain ratio between the wave size of the piston and the angle of inclination of the wedge, it is possibleto have a minimum in the directional chart along the axis of symmetry of the wedge. Calculations ofthe pressure modulus in the vicinity of the piston are performed, which illustrate how the failure in the directional chart in the direction of the waveguide axis is gradually formed.
Pages of the article in the issue: 34 - 37
Language of the article: UkrainianIn the work the task of radiation of a at piston in a wedge-shaped waveguide is considered. The peculiarities of the radiation of a at piston into a wedge-shaped waveguide depending on the parametersof the task, namely, the angle of inclination of the wedge and the wave size of the piston, that is theratio of the piston length to the wavelength it emits, are investigated. The directional charts of a atpiston in a wedge-shaped waveguide at dierent angles of the wedge are calculated. It is shown that at acertain ratio between the wave size of the piston and the angle of inclination of the wedge, it is possibleto have a minimum in the directional chart along the axis of symmetry of the wedge. Calculations ofthe pressure modulus in the vicinity of the piston are performed, which illustrate how the failure in thedirectional chart in the direction of the waveguide axis is gradually formed
Hereditary creep of isotropic composites of random structure under a complex stress state
Get PDFNonlinear hereditary creep problem of the mechanics of composites is solved within the framework of a second-order theory. The hereditary functionals are used to construct general constitutive relations. A stochastic boundary value problem for determining the stress concentration and its relaxation in metal matrix composite (PMC) is solved in Laplace-Carson image space. Shapery\u27s correspondence principle for quasi-linear viscoelastic media is generalised on the hereditary creep problem and the method of successive approximation is used. The reduced creep functions and the stress concentration parameters are determined. Examples are given showing the importance of the mutual influence of nonlinear elastic and viscous properties of the components on stress redistribution near inclusions with possibility to predicting the long-term strength.
Pages of the article in the issue: 77 - 80
Language of the article: Ukrainia
A statistical algorithm for fast estimation of heart rate and localization of cardiac sounds in phonocardiograms recorded by electronic stethoscopes
Get PDFA draft version of the algorithm for fast determination of duration of the systolic and diastolic phases of the cardiac cycle based on a statistical analysis of a digital phonocardiogram is presented. The developed technique includes localization of the cardiac tones in the record by a quantile dichotomy and modal analysis of the calculated time intervals between the adjacent detected peaks. Next, the scatter plot is constructed in terms of time intervals before and after each peak. The stability of the cardiac rhythm is determined by the density of the cluster occurring near the cross-section of two modal values plotted along the axes. At dominance of a cardiac component in the signal, the discussed approach allows quite reliable determination of the moments of the emergence of the first and second cardiac sounds tones practically on each of the cardiac cycles. This opens the possibility to analyze the variation in the duration of separate phases of heart contractions over time. Due to the work directly in the time domain and low computational costs, the algorithms of this class are suitable for application in portable diagnostic systems with limited processor power.
Pages of the article in the issue: 81 - 84
Language of the article: Englis
Numerical solution of a singular integral equation related with a dynamic contact interaction problem
Get PDFA singular integral equation with a fixed singularity to which the problem of contact interaction of two quarters of spaces in the conditions of harmonic oscillations of longitudinal shear is reduced is considered. A quarters of the space is situated so that the half-space composed of them has a stepped boundary. In the contact area, the conditions for ideal coupled are satisfied. The unknown function in this equation is the contact stresses. For the numerical solution of this equation, a method that takes into account the asymptotic behavior of contact stresses at the edge point is proposed. The basis of this method is the use of special quadrature formulas for singular integrals obtained in the article. When obtaining these formulas, the unknown function was approximated by an interpolation polynomial, in which the roots of the Laguerre polynomials are the points of interpolation. The values of the unknown function at the interpolation points are found by the collocation method, herewith the collocation points of collocationare the roots of the special function. An approximate formula for calculating contact stresses can have practical application. The effectiveness of the proposed method is demonstrated by the numerical example.
Pages of the article in the issue: 93 - 96
Language of the article: Ukrainia
Comparative analysis of the linear and nonlinear rules of mixtures in modeling the stress state of a half-space
Get PDFIn the present work we solve the axially symmetric problem of a half-space under thermal loading. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner–Partom unified model of flow generalized in the case of microstructure influence on inelastic characteristics of steel. To determine the parameters of the model corresponded to yield stress and yield strength the mixture rule is utilized. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. Equations of the evolution for the inelastic flow model are integrated by the second-order Euler implicit method. The equations of motion are integrated by the Newmark method, whereas the heat-conduction equation is integrated by the first-order implicit method. We use quadrangular isoparametric elements. The parameters of a fine grid are chosen with the help of the criterion of practical convergence of the solutions. The stress state taking into account linear and nonlinear rules of mixtures is described.
Pages of the article in the issue: 94 - 97
Language of the article: Ukrainia
Simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion
Get PDFIn the paper, we consider the problem of simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly ?-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when ?(x) = (|x|^p)/p, |x| ? 1, p > 1. In order to obtain these results, we use some results from the theory of ?-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
Pages of the article in the issue: 11 - 19
Language of the article: UkrainianIn the paper, we consider the problem of simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly ?-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when ?(x) = (|x|^p)/p, |x| ? 1, p > 1. In order to obtain these results, we use some results from the theory of ?-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
Pages of the article in the issue: 11 - 19
Language of the article: Ukrainia
Review of neural approaches for conditional text generation
Get PDFThe article is devoted to the review of conditional test generation, one of the most promising fields of natural language processing and artificial intelligence. Specifically, we explore monolingual local sequence transduction tasks: paraphrase generation, grammatical and spelling errors correction, text simplification. To give a better understanding of the considered tasks, we show examples of good rewrites. Then we take a deep look at such key aspects as publicly available datasets with the splits (training, validation, and testing), quality metrics for proper evaluation, and modern solutions based primarily on modern neural networks. For each task, we analyze its main characteristics and how they influence the state-of-the-art models. Eventually, we investigate the most significant shared features for the whole group of tasks in general and for approaches that provide solutions for them.
Pages of the article in the issue: 102 - 107
Language of the article: Ukrainia
Parameter of thermal rectification in the bimaterial with interfacial cracking
Get PDFThe phenomenon of thermal rectification in bi-material with a periodic system of gas-filled interfacial cracks has been studied. The change of thermal resistance and pressure of the crack filler under the action of tensile forces and uniform heat flow is taken into account. The gas pressure is determined from the Clapeyron-Mendeleev equation. The thermal resistance of the gas is directly proportional to the opening of the cracks and inversely proportional to the thermal conductivity of the gas. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for an opening cracks and a temperature jump between the cracks faces. An analytical-numerical iterative procedure is proposed to solve the system of singular integro-differential equations. The parameter of thermal rectification is determined and its dependence on the applied on the thermal and mechanical loads, thermal conductivity and mass of the gas and the interfacial cracking factor of the bi-material is analyzed. The nonlinear dependence of the thermal rectification parameter on the heat flow density and the interfacial cracking factor is established. The thermal rectification is manifested to a greater extent for higher values of heat flow and lower thermal conductivity of gas.
Pages of the article in the issue: 119 - 122
Language of the article: Ukrainia
Modelling of cyclic creep deformations of nonlinear viscoelastic materials using Heaviside function
Get PDFThe problem of calculating the deformations of the cyclic creep of nonlinear viscoelastic materials is considered, which is given in the form of cyclic alternations of loads and unloadings of equal amplitude over rectangular cycles, where the duration of loading and unloading half-cyclescoincide. The program of loading is realized in the form of sequence of elementary loadings set by means of unit functions of Heaviside. A nonlinear creep model with a time-independent nonlinearity of Yu. Rabotnov\u27s model is used to describe the deformation process. The fractional-exponential function is used as the nucleus of heredity. The paper develops a nonlinear viscosity model with time-independent nonlinearity due to the use of instantaneous deformation diagrams as isochronous for zero time and smoothing cubic splines, as approximations of nonlinear instantaneous deformation diagrams that define the nonlinearity of the model. The concept of a single isochronous deformation diagram for the studied material is experimentally substantiated. A system of solution equations of nonlinear creep under cyclic loading is formulated. The problem of calculating the deformations of stationary and cyclic creep for nylon fibers FM 10001 is solved and experimentally tested.
Pages of the article in the issue: 62 - 65
Language of the article: UkrainianThe problem of calculating the deformations of the cyclic creep of nonlinear viscoelastic materials is considered, which is given in the form of cyclic alternations of loads and unloadings of equal amplitude over rectangular cycles, where the duration of loading and unloading half-cyclescoincide. The program of loading is realized in the form of sequence of elementary loadings set by means of unit functions of Heaviside. A nonlinear creep model with a time-independent nonlinearity of Yu. Rabotnov\u27s model is used to describe the deformation process. The fractional-exponential function is used as the nucleus of heredity. The paper develops a nonlinear viscosity model with time-independent nonlinearity due to the use of instantaneous deformation diagrams as isochronous for zero time and smoothing cubic splines, as approximations of nonlinear instantaneous deformation diagrams that define the nonlinearity of the model. The concept of a single isochronous deformation diagram for the studied material is experimentally substantiated. A system of solution equations of nonlinear creep under cyclic loading is formulated. The problem of calculating the deformations of stationary and cyclic creep for nylon fibers FM 10001 is solved and experimentally tested.
Pages of the article in the issue: 62 - 65
Language of the article: Ukrainia